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Simplifying 0.5x2 + -16x + -5 = 0 Reorder the terms: -5 + -16x + 0.5x2 = 0 Solving -5 + -16x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -10 + -32x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -32x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -32x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -32x + x2 = 0 + 10 -32x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -32x + x2 = 10 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 10 + 256 Reorder the terms: 256 + -32x + x2 = 10 + 256 Combine like terms: 10 + 256 = 266 256 + -32x + x2 = 266 Factor a perfect square on the left side: (x + -16)(x + -16) = 266 Calculate the square root of the right side: 16.30950643 Break this problem into two subproblems by setting (x + -16) equal to 16.30950643 and -16.30950643.Subproblem 1
x + -16 = 16.30950643 Simplifying x + -16 = 16.30950643 Reorder the terms: -16 + x = 16.30950643 Solving -16 + x = 16.30950643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 16.30950643 + 16 Combine like terms: -16 + 16 = 0 0 + x = 16.30950643 + 16 x = 16.30950643 + 16 Combine like terms: 16.30950643 + 16 = 32.30950643 x = 32.30950643 Simplifying x = 32.30950643Subproblem 2
x + -16 = -16.30950643 Simplifying x + -16 = -16.30950643 Reorder the terms: -16 + x = -16.30950643 Solving -16 + x = -16.30950643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -16.30950643 + 16 Combine like terms: -16 + 16 = 0 0 + x = -16.30950643 + 16 x = -16.30950643 + 16 Combine like terms: -16.30950643 + 16 = -0.30950643 x = -0.30950643 Simplifying x = -0.30950643Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.30950643, -0.30950643}
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